| $${\theta}$$ | sin | cos | tan |
|---|---|---|---|
| 9 | $${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$ | $${\frac{\sqrt{8 + 2 \sqrt{10 + 2 \sqrt{5}}}}{4}}$$ | $${\sqrt{5} + 1 - \sqrt{5 + 2 \sqrt{5}}}$$ |
| 15 | $${\frac{\sqrt{6} - \sqrt{2}}{4}}$$ | $${\frac{\sqrt{6} + \sqrt{2}}{4}}$$ | $${2 - \sqrt{3}}$$ |
| 18 | $${\frac{\sqrt{5} - 1}{4}}$$ | $${\frac{\sqrt{10+2\sqrt{5}}}{4}}$$ | $${\frac{\sqrt{5 - 2 \sqrt{5}}}{\sqrt{5}}}$$ |
| 22.5 | $${\frac{\sqrt{2-\sqrt{2}}}{2}}$$ | $${\frac{\sqrt{2+\sqrt{2}}}{2}}$$ | $${\sqrt{2} - 1}$$ |
| 27 | $${\frac{\sqrt{8 - 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$ | $${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$ | $${\sqrt{5} - 1 - \sqrt{5 - 2 \sqrt{5}}}$$ |
| 30 | $${\frac{1}{2}}$$ | $${\frac{\sqrt{3}}{2}}$$ | $${\frac{\sqrt{3}}{3}}$$ |
| 36 | $${\frac{\sqrt{10-2\sqrt{5}}}{4}}$$ | $${\frac{\sqrt{5} + 1}{4}}$$ | $${\sqrt{5 - 2 \sqrt{5}}}$$ |
| 45 | $${\frac{\sqrt{2}}{2}}$$ | $${\frac{\sqrt{2}}{2}}$$ | $${1}$$ |
| 54 | $${\frac{\sqrt{5} + 1}{4}}$$ | $${\frac{\sqrt{10-2\sqrt{5}}}{4}}$$ | $${\frac{\sqrt{5 + 2 \sqrt{5}}}{\sqrt{5}}}$$ |
| 60 | $${\frac{\sqrt{3}}{2}}$$ | $${\frac{1}{2}}$$ | $${\sqrt{3}}$$ |
| 63 | $${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$ | $${\frac{\sqrt{8 - 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$ | $${\sqrt{5} - 1 + \sqrt{5 - 2 \sqrt{5}}}$$ |
| 72 | $${\frac{\sqrt{10+2\sqrt{5}}}{4}}$$ | $${\frac{\sqrt{5} - 1}{4}}$$ | $${\sqrt{5 + 2 \sqrt{5}}}$$ |
| 75 | $${\frac{\sqrt{6} + \sqrt{2}}{4}}$$ | $${\frac{\sqrt{6} - \sqrt{2}}{4}}$$ | $${2 + \sqrt{3}}$$ |
| 81 | $${\frac{\sqrt{8 + 2 \sqrt{10 + 2 \sqrt{5}}}}{4}}$$ | $${\frac{\sqrt{8 + 2 \sqrt{10 - 2 \sqrt{5}}}}{4}}$$ | $${\sqrt{5} + 1 + \sqrt{5 + 2 \sqrt{5}}}$$ | 90 | $${1}$$ | $${0}$$ | $${\infty}$$ |
| 105 | $${\frac{\sqrt{6} + \sqrt{2}}{4}}$$ | $${\frac{-\sqrt{6} + \sqrt{2}}{4}}$$ | $${-2 - \sqrt{3}}$$ | 120 | $${\frac{\sqrt{3}}{2}}$$ | $${-\frac{1}{2}}$$ | $${-\sqrt{3}}$$ |
| 135 | $${\frac{\sqrt{2}}{2}}$$ | $${-\frac{\sqrt{2}}{2}}$$ | $${-1}$$ |
| 150 | $${\frac{1}{2}}$$ | $${-\frac{\sqrt{3}}{2}}$$ | $${-\frac{\sqrt{3}}{3}}$$ |
| 180 | $${0}$$ | $${-1}$$ | $${0}$$ |
| 210 | $${-\frac{1}{2}}$$ | $${-\frac{\sqrt{3}}{2}}$$ | $${\frac{\sqrt{3}}{3}}$$ |
| 225 | $${-\frac{\sqrt{2}}{2}}$$ | $${-\frac{\sqrt{2}}{2}}$$ | $${1}$$ |
| 240 | $${-\frac{\sqrt{3}}{2}}$$ | $${-\frac{1}{2}}$$ | $${\sqrt{3}}$$ | 270 | $${-1}$$ | $${0}$$ | $${-\infty}$$ |
| 300 | $${-\frac{\sqrt{3}}{2}}$$ | $${\frac{1}{2}}$$ | $${-\sqrt{3}}$$ |
| 315 | $${-\frac{\sqrt{2}}{2}}$$ | $${\frac{\sqrt{2}}{2}}$$ | $${-1}$$ |
| 330 | $${-\frac{1}{2}}$$ | $${\frac{\sqrt{3}}{2}}$$ | $${-\frac{\sqrt{3}}{3}}$$ |